The Simplest Ancient Math Problem No One Could Solve

Join my mailing list! https://ben-syversen.kit.com Go to https://cyberghostvpn.com/BenSyversen to get 84% off from this video's sponsor, CyberGhost VPN, with 4 months free! Ancient Greek mathematicians wrestled for centuries with a seemingly pointless problem that led them to rich mathematical discoveries. ____ Join my Patreon for early previews, ad free versions of the videos, and to support the channel!   / bensyversen   Or, support me on Ko-Fi with a one-time donation: https://ko-fi.com/bensyversen Here is a music-free version of this video, if you prefer:   / simplest-ancient-146310621   ______ Credits: Written, recorded, edited, animated by Ben Syversen Illustrations by Alex Zepherin/Don Dada Studios Additional illustrations by Kendall Eddy Special thanks to Viktor Blåsjö for his feedback and for answering my many questions about this topic. Thanks to @Aleph0 for letting use a few clips from his wonderful recent video about the Twin Prime Conjecture:    • Something strange happens when you look at...   Additional thank you to ‪@SimonUbsdell‬ and ‪@Deepia-ls2fo‬ for helping me with Blender, and ‪@twoswap‬ for help with some LaTeX animations. ______ Sources and recommended reading: Operationalism: An Interpretation of the Philosophy of Ancient Greek Geometry, Viktor Blåsjö: https://link.springer.com/article/10.... “Science Awakening,” B.L. Van der Waerden “A History of Greek Mathematics,” Thomas Heath “The Ancient Tradition of Geometric Problems” Wilbur Knorr For a good summary of the conics of Apollonius, which my parabola explanation is based on, read: “A History of Mathematics, An Introduction” by Victor J Katz 3d print your own conic compass! https://www.instructables.com/The-Los... Music from Epidemic Sound Except where indicated on screen, additional images are public domain or licensed via Envato Elements Time stamps: 00:00 Intro 01:30 History of Numbers 05:03 Straightedge and Compass Constructions 07:35 Doubling the Cube 10:22 Archytas' Solution 15:18 Eudoxus' Solution 15:37 Menaechmus' Solution 20:26 Conic Sections and Conic Compasses 22:15 Other Solutions and Other Problems 23:59 The Delians 24:32 Modern Analogies